WNCP and similar curricula avoid mention of the standard algorithms of elementary arithmetic:
- addition down columns, with “carry”;
- subtraction similarly, with “borrow”;
- multiplication arranged vertically by columns with the usual procedure; and
- long division.
Or, if they mention them, such mention is either negative, or come with warnings reminiscent of those you might see on dangerous household cleaners, or suggest that, while they may be used or even taught, this must always happen after “understanding” or with no better than equal status as one of several “strategies”, and generally very late in the learning curve.
This comes as a shock to anyone unfamiliar with trends in math education, and you may wonder why. The idea that teaching the algorithms is, or may be, harmful to children’s development seems to come out of some strange ideas associated with the theories of French educational theorist Jean Piaget and an old pedagogical methodology often called “constructivism” (not to be confused with an unrelated, respectable theory of learning in psychology that goes by the same name) which dictates that the best way to “teach” is not to teach, but to allow students to discover things for themselves. Kirschner et al provide a good summary of research demonstrating the problems with constructivist teaching (which they refer to as “minimal guidance instruction”).
The particular doctrine of “no standard algorithms” or more generally “no algorithms” had no empirical supporting data of note until a study done in the mid-90s by Kamii and Dominick, who were outspoken advocates of this system. Their article, The Harmful Effects of Algorithms in Grades 1-4, published by the NCTM in 1998, purports to supply the missing data. An early description of the same study, To teach or not to teach algorithms, is available on the internet.
The Kamii and Dominick study is cited widely to justify the elimination of the algorithms. In the WNCP K-9 framework document a citation is found on p. 163.
Recently Bill Quirk, who writes independently about the problems of current math education trends, has written a hard-hitting critique of the Kamii and Dominick study, hitting on some serious problems with it. Another discussion of why this study should not be taken seriously may be found on blog Do the Math. The conclusions of each of these critiques is compelling but it must be said that they are only summaries — still other methodological problems in the Kamii and Dominick study might be mentioned. This matter is commended to the attention of anyone with an interest in the roots of the anti-algorithm ideology in our schools.